Germany still have plenty of room for improvement after easing into the Euro 2016 quarter-finals by beating Slovakia 3-0 on Sunday, coach Joachim Loew warned.

The reigning world champions were comfortable winners in their last-16 clash in Lille as Jerome Boateng, Mario Gomez and the excellent Julian Draxler all scored while Mesut Ozil had an early penalty saved.

“We put in a great effort, both defensively and going forward, but with all due respect to our opponents we cannot say from this that we are going to dominate the competition. We will have to improve to win the tournament,” said Loew.

Germany will face either reigning European champions Spain or old rivals Italy in Bordeaux in the last eight next weekend but Loew said he is not worried about who his side meet next.

“I am sleeping well. Both teams are among the favourites. Italy are incredibly strong defensively while Spain are the best attacking side we have seen in recent years.

“We have to improve if we want to compete with the other teams to win the title. Our task now will be more difficult and we cannot leave our opponents any spaces because teams will punish us. We also have to take our chances in the games we have coming up.”

The main source of satisfaction so far for Loew has been in defence with Germany having reached the last eight without conceding a goal in any of their four matches at the tournament.

“I am happy the defence has performed so well so far but now we will come up against much more dangerous sides who have top strikers,” Loew added before heaping praise on Boateng, whose goal was his first for his country on the occasion of his 63rd cap.

“There is no need to say anything more about his value to us. That has been clear for years now.

“The defence was excellent today. Boateng and (Mats) Hummels won almost every challenge, they were focused, they helped build the play and then Boateng scored the goal.”

Bayern Munich stopper Boateng had been a slight doubt ahead of the match due to a calf knock that forced him off in the 1-0 win against Northern Ireland.

He was substituted in the second half on Sunday along with midfielder Sami Khedira in order to prevent either player collecting a yellow card that would have seen them suspended for the quarter-finals.

“I am happy that his calf was okay. He is a player the side trusts,” added Loew of Boateng.

Loew had been unhappy with his team’s finishing during the group stage and he opted to drop the underperforming Mario Goetze as Draxler, of Wolfsburg, started in the only change from their 1-0 win against Northern Ireland.

Slovakia have a recent history of pulling off surprise results, from their defeat of Spain in qualifying to the recent friendly victory in Germany and the goalless draw with England that saw them progress from the group stage.

But their hopes of another day to remember were rapidly nipped in the bud by the world champions, who underlined their credentials and sent a clear message to their Euro rivals.

Sami Khedira was first to threaten with a header from a Toni Kroos free-kick that was tipped over by Slovakian ‘keeper Matus Kozacik, and from the corner that followed Germany were in front.

Kroos’ delivery from the German left was headed out by Milan Skriniar but the ball fell for Boateng on the edge of the box and the Bayern Munich stopper met it on the volley, finding the bottom-left corner with the aid of a small deflection off the unfortunate Skriniar.

Slovakia were overwhelmed and they conceded a penalty in the 13th minute when skipper Martin Skrtel grappled with Gomez as the two went for a high ball in the box.

Skrtel was booked for his intervention, but Slovakia were let off the hook as Ozil’s kick was well saved by Kozacik diving to his left.

Excluding shoot-outs, it was the first penalty missed by a German player in a European Championship finals match.

The miss did nothing to halt Germany’s momentum, though, and it remained one-way traffic.

Germany went on to increase their lead as Draxler combined with Jonas Hector down the left before heading for the byline and cutting the ball back for Gomez to finish at the near post.

And, if there were any lingering doubts about the outcome, Germany put the game to bed on 63 minutes, Hummels heading down a corner for Draxler, who volleyed in at the back post to get the goal his performance deserved.